What is (\partial)/(\partial x)((z)(4x^2y+3y-5)) ?

The answer to (\partial)/(\partial x)((z)(4x^2y+3y-5)) is 8zxy

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(\partial)/(\partial x)((z)(4x^2y+3y-5))

\frac{\partial}{\partial x} ((z) (4 x^{2} y + 3 y - 5))

8 z x y

Solution steps

\frac{\partial}{\partial x} ((z) (4 x^{2} y + 3 y - 5))

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial x} (4 x^{2} y + 3 y - 5)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (\frac{\partial}{\partial x} (4 x^{2} y) + \frac{\partial}{\partial x} (3 y) - \frac{\partial}{\partial x} (5))

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

\frac{\partial}{\partial x} (3 y) = 0

\frac{\partial}{\partial x} (5) = 0

= z (8 y x + 0 - 0)

Simplify

= 8 z x y

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(x_{0} + e x_{1} + x_{2} e^{2})^{3}

What is (\partial)/(\partial x)((z)(4x^2y+3y-5)) ?
The answer to (\partial)/(\partial x)((z)(4x^2y+3y-5)) is 8zxy